Classical Limit for Scalar Fields at High Temperature

TL;DR

This paper demonstrates that at high temperatures, the behavior of soft modes in scalar quantum field theories can be effectively described by classical statistical field theory, with quantum coherence loss due to thermal bath interactions.

Contribution

It provides a detailed analysis of the classical limit for scalar fields at high temperature, including an effective theory for soft modes and quantifies quantum corrections.

Findings

Soft modes are governed by classical statistical field theory.

Quantum coherence loss is caused by interactions with thermal bath modes.

The plasmon damping rate is explicitly calculated.

Abstract

We study real-time correlation functions in scalar quantum field theories at temperature $T=1/\beta$. We show that the behaviour of soft, long wavelength modes is determined by classical statistical field theory. The loss of quantum coherence is due to interactions with the soft modes of the thermal bath. The soft modes are separated from the hard modes by an infrared cutoff $\L \ll 1/(\hbar\beta)$. Integrating out the hard modes yields an effective theory for the soft modes. The infrared cutoff $\L$ controls corrections to the classical limit which are $\cO{\hbar\beta\L}$. As an application, the plasmon damping rate is calculated.